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I just got back from seeing a friend off at the airport.
Literal
Friend [object-を] see-off-[purpose-に] airport-until go-[come-back-てきた]-just-[place-ところです].
~たところです marks the 'just now' aspect — an action completed in the very recent past. 見送りに ('for the purpose of seeing off') uses the masu-stem 見送り as a noun + purpose-に. まで marks the extent of the journey ('all the way to the airport'). The whole sentence packs several grammar points into one natural statement.